Proc nlin with weights and SSE

[RB_Wouter]

Hi

I have a problem estimating a nlin function on weighted data which basically comes down to the problem below:

Consider the following data where clearly y =x² and z aresome weights. Bij adapting the standard proc nlin to include the weights:

data STARTDATA;
input x  y z ;
datalines ;
1 2 0.1
2 4 0.2 
3 9 0.2 
4 16 0.5 
; 
PROC SQL;
	CREATE VIEW WORK.SORTTempTableSorted AS
		SELECT T.y, T.x, T.z
	FROM WORK.STARTDATA as T;
PROC NLIN DATA=WORK.SORTTempTableSorted
	MAXITER=100
	CONVERGE=1E-05
		SINGULAR=1E-08
	MAXSUBIT=30;
	_WEIGHT_ = z;
	MODEL y = x ** b
	;
	PARMS
	b=0.01;
RUN;

 The parameter b is estimated correctly as 2. However the SSE is minimized to the first weight which is 0.1 and is not further decreased to  0.
This makes the R²  (here 1) wrongly estimated.

How can I correct my example such that the SSE can be smaller than the first weight?

Thanks in advance

[lvm]

Why do you think the results are wrong? I just ran your program with plots turned on, and everything looks fine for the fit. Taking out the weight statement gives a different confidence region, different SE, etc.,as expected. I think you just have a coincidence about the "0.1". For instance, I ran:

data b; set startdata;
pred = x**2;
SS = (y - pred)**2;
WSS = z*SS;
run;
proc means data=b  sum;
var SS WSS;
run;

To manually get the sum of squares, weighted and unweighted, based on your parameter estimate. Weighted SS = 0.1, just like the NLIN output. If you run NLIN without the weight, you get SS = 1.0. This is what you get manually (above). I think everything is fine. By the way, put a plots=all option in your NLIN statement for good graphs.

[lvm · Accepted solution]

Forgot the mention above, your SS should not be 0 because your y values are not exactly equal to x**2 (the first y should be 1, not 2, if you want an exact match).

[RB_Wouter]

Hi

There is an input error in my trial model: y1 should be 1 of course. However In my real problem this gives still some strange results. Thanks for the plots =all. It helps for my real problem